MODELING FINGER DEVELOPMENT AND PERSISTENCE IN INITIALLY DRY POROUS-MEDIA

The mechanism for the growth and persistence of gravity-driven fingere d flow of water in initially dry porous media is described. A Galerkin finite element solution of the two-dimensional Richards equation with the associated parameter equations for capillary hysteresis in the wa ter retention function is presented. A scheme for upstream weighting o f internodal unsaturated hydraulic conductivities is applied to limit smearing of steep wetting fronts. The growth and persistence of a sing le finger in an initially dry porous media is simulated using this num erical solution scheme. To adequately simulate fingered flow, it was f ound that the upstream weighting factor had to be negative, meaning th at the internodal unsaturated hydraulic conductivities were weighted m ore by the downstream node. It is shown that the growth and persistenc e of a finger is sensitive to the character of the porous media water retention functions. For porous media where the water-entry capillary pressure on the main wetting function is less than the air-entry capil lary pressure on the main drainage function, a small perturbation will grow into a finger, and during sequential drainage and wetting the fi nger will persist. In contrast, for porous media where the water-entry capillary pressure on the main wetting function is greater than the a ir-entry capillary pressure on the main drainage function, the same sm all perturbation will dissipate by capillary diffusion. The finger wid ths derived from the numerical simulation are similar to those predict ed by analytical theory.